1. Field of the Invention
This invention relates to quantum computing and to solid-state devices that use superconductive materials to implement the coherent quantum states used in quantum computing.
2. Description of Related Art
Research on what is now called quantum computing traces back to Richard Feynman. See, e.g., R. P. Feynman, Int. J. Theor. Phys. 21, 467 (1982). He noted that quantum systems are inherently difficult to simulate with classical (i.e., conventional, non-quantum) computers, but that this task could be accomplished by observing the evolution of another quantum system. In particular, solving a theory for the behavior of a quantum system commonly involves solving a differential equation related to the system""s Hamiltonian. Observing the behavior of the system provides information regarding the solutions to the equation.
Further efforts in quantum computing were initially concentrated on building the formal theory or on xe2x80x9csoftware developmentxe2x80x9d or extension to other computational problems. Milestones were the discoveries of the Shor and Grover algorithms. See, e.g., P. Shor, SIAM J. of Comput. 26, 1484 (1997); L. Grover, Proc. 28th STOC, 212 (ACM Press, New York, 1996); and A. Kitaev, LANL preprint quant-ph/9511026. In particular, the Shor algorithm permits a quantum computer to factorize large natural numbers efficiently. In this application, a quantum computer could render obsolete all existing xe2x80x9cpublic-keyxe2x80x9d encryption schemes. In another application, quantum computers (or even a smaller-scale device such as a quantum repeater) could enable absolutely safe communication channels where a message, in principle, cannot be intercepted without being destroyed in the process. See, e.g., H. J. Briegel et al., preprint quant-ph/9803056 and references therein.
Showing that fault-tolerant quantum computation is theoretically possible opened the way for attempts at practical realizations. See, e.g., E. Knill, R. Laflamme, and W. Zurek, Science 279, 342 (1998).
Quantum computing generally involves initializing the states of N qubits (quantum bits), creating controlled entanglements among them, allowing these states to evolve, and reading out the qubits the states evolve. A qubit is conventionally a system having two degenerate (i.e., of equal energy) quantum states, with a non-zero probability of being found in either state. Thus, N qubits can define an initial state that is a combination of 2N classical states. This entangled initial state undergoes an evolution, governed by the interactions that the qubits have among themselves and with external influences. This evolution of the states of N qubits defines a calculation or in effect, 2N simultaneous classical calculations. Reading out the states of the qubits after evolution is complete determines the results of the calculations.
Several physical systems have been proposed for the qubits in a quantum computer. One system uses molecules having degenerate nuclear-spin states. See N. Gershenfeld and I. Chuang, xe2x80x9cMethod and Apparatus for Quantum Information Processing,xe2x80x9d U.S. Pat. No. 5,917,322. Nuclear magnetic resonance (NMR) techniques can read the spin states. These systems have successfully implemented a search algorithm, see, e.g., M. Mosca, R. H. Hansen, and J. A. Jones, xe2x80x9cImplementation of a quantum search algorithm on a quantum computer,xe2x80x9d Nature 393, 344 (1998) and references therein, and a number-ordering algorithm, see, e.g., L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, R. Cleve, and I. L. Chuang, xe2x80x9cExperimental realization of order-finding with a quantum computer,xe2x80x9d preprint quant-ph/0007017 and references therein. (The number-ordering algorithm is related to the quantum Fourier transform, an essential element of both Shor""s factoring algorithm and Grover""s algorithm for searching unsorted databases.) However, expanding such systems to a commercially useful number of qubits is difficult.
More generally, many of the current proposals will not scale up from a few qubits to the 102xcx9c103 qubits needed for most practical calculations. A technology that is excellently suited for large-scale integration involves superconducting phase qubits.
One implementation of a phase qubit involves a micrometer-sized loop with three (or four) Josephson junctions. See J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd, xe2x80x9cJosephson Persistent-Current Qubit,xe2x80x9d Science 285, 1036 (1999) and references therein. The energy levels of this system correspond to differing amounts of magnetic flux threading the loop. Application of a static magnetic field normal to the loop may bring two of these energy levels (or basis states) into degeneracy. Typically, external AC electromagnetic fields are also applied, to enable tunneling between non-degenerate states.
A radio-frequency superconducting quantum-interference device (rf-SQUID) qubit is another type of phase qubit having a state that can be read by inductively coupling the rf-SQUID to rapid single-flux-quantum (RSFQ) circuitry. See R. C. Rey-de-Castro, M. F. Bocko, A. M. Herr, C. A. Mancini, and M. J. Feldman, xe2x80x9cDesign of an RSFQ Control Circuit to Observe MQC on an rf-SQUID,xe2x80x9d IEEE Trans. Appl. Supercond. 11, 1014 (2001) and references therein, which is hereby incorporated by reference in its entirety. A timer controls the readout circuitry and triggers the entire process with a single input pulse, producing an output pulse only for one of the two possible final qubit states. The risk of this readout method lies in the inductive coupling with the environment causing decoherence or disturbance of the qubit state during quantum evolution. The circuitry attempts to reduce decoherence by isolating the qubit with intermediate inductive loops. Although this may be effective, the overhead is large, and the method becomes clumsy for large numbers of qubits.
In both above systems, an additional problem is the use of basis states that are not naturally degenerate. Accordingly, the strength of the biasing field for each qubit has to be precisely controlled to achieve the desired tunneling between its basis states. This is possible for one qubit, but becomes extremely difficult with several qubits.
U.S. patent application Ser. Nos. 09/452,749, xe2x80x9cPermanent Readout Superconducting Qubit,xe2x80x9d filed Dec. 1, 1999, and Ser. No. 09/479,336, xe2x80x9cQubit using a Josephson Junction between s-Wave and d-Wave Superconductors,xe2x80x9d filed Jan. 7, 2000, which are hereby incorporated by reference in their entirety, describe Permanent Readout Superconducting Qubits (PRSQs). An exemplary PRSQ consists of a bulk superconductor, a grain boundary, a superconductive mesoscopic island [i.e., a superconductive region having a size such that a single excess Cooper pair (pair of electrons) is noticeable], and a means for grounding the island. The material used in the bulk or the island has a superconducting order containing a dominant component whose pairing symmetry has non-zero angular momentum, and a sub-dominant component with any pairing symmetry As a result, the qubit has the states xc2x1"PHgr"0, where "PHgr"0 is the minimum-energy phase of the island with respect to the bulk superconductor.
The area in which the phase is maintained is much more localized in a PRSQ than in prior qubits such as an rf-SQUID qubit. Thus, the rate of decoherence is minimized, making the PRSQ a strong candidate for future solid-state quantum-computing implementations.
The state of a PRSQ can be characterized by the direction of the magnetic field, H↑ or H↓ inside the junction between the bulk and the island. This difference in field direction can be used to read out the state of a PRSQ, for instance using a SQUID. However, the proposed readout methods introduce an interaction with the environment that potentially disturbs the state of the qubit, which necessitates complicated and time-consuming error-correction and/or re-initialization procedures. Attempts to xe2x80x9cswitch offxe2x80x9d the readout circuit during quantum evolution face severe practical constraints. For example, physically manipulating the distance between the SQUID and qubit prior to readout could provide the desired coupling and decoupling but is complex to implement, while up to the present, no integrated solid-state alternative method is known.
The issues discussed above for rf-SQUID qubits and PRSQs are general. Also, other currently proposed methods for reading out the state of a phase qubit involve detection and manipulation of magnetic fields, which make these methods susceptible to decohering noise and limit the overall scalability of the device. Thus, there is a need for an efficient readout method that is non-destructive and switchable, i.e., that does not couple the qubit to the environment during computations.
Our invention invokes the classical Hall effect, which arises from the tangential acceleration of moving charged particles in an external magnetic field perpendicular to the velocity of the charged particles. The Hall effect drives oppositely charged particles in opposite directions and leading to charge build-up on the surfaces. As a result, current flow through a sample in a magnetic field produces a Hall voltage across the sample, in the direction perpendicular to both the current and the field. The Hall effect can be observed in a sample that is a conductor or a semiconductor, in which case the charged particles are the electrons or holes.
The Hall effect can also exist in superconducting structures. For SNS (superconductor-normal conductor-superconductor) junctions, the Hall effect was theoretically described by F. Zhou and B. Spivak in xe2x80x9cHall Effect in SN and SNS Junctions,xe2x80x9d Phys. Rev. Lett. 80, 3847 (1998); for a related effect, see A. Furusaki, M. Matsumoto, and M. Sigrist, xe2x80x9cSpontaneous Hall effect in chiral p-wave superconductor,xe2x80x9d preprint cond-mat/0102143 and references therein. Both articles are hereby incorporated by reference in their entirety.
In accordance with an aspect of the invention, a phase-qubit device such as a PRSQ uses a four-terminal readout method and system. One embodiment includes an insulator over the qubit and conducting electrodes (which can be metallic) over the insulator (or two insulators over the qubit with an electrode over each insulator) to create two extra tunnel junctions across the width of the qubit. A readout process then involves grounding the PRSQ island, applying a current bias through the qubit, and measuring the potential drop across the electrodes.
The above embodiment of the invention can take advantage of the Hall effect to measure the magnetic field inside the junction. The current bias perpendicular to the junction (from bulk to island for example) can be a pulse. Given the direction of the bias current, the sign of the time-averaged Hall voltage read out across the width of the junction indicates the orientation of the magnetic field, i.e., the state of the qubit. In other words, for a given bias current, the expected voltage is positive or negative depending on the qubit state (H↑ or H↓).
Before reading out the qubit state, the qubit island is grounded for the application of the bias current through the qubit. The grounding operation strongly increases the island capacitance of the island, thus xe2x80x9cfreezingxe2x80x9d the qubit by suppressing tunneling and other quantum effects. Thus, while the grounding connection is closed, the qubit retains the same state. In an embodiment of the invention, the grounding circuitry includes a switch such as a single-electron transistor (SET) or parity key. By modulating the gate voltage on the SET (or the flux through the parity key), the circuit can be opened and closed The SET can operate with either single electrons or Cooper pairs, depending on the embodiment of the invention.
In one embodiment of the invention, the Josephson junction in the qubit is an SNS structure, in which case the Hall voltage in the normal-conductor barrier consists of short pulses with a non-zero time average. More generally, readout processes using the Hall effect are applicable to any type of Josephson junction including, for example, grain-boundary junctions.
In an embodiment of the invention, the resistance of the tunnel barrier that isolates the qubit from an electrode in the readout system is chosen so as to allow for voltage measurements without introducing a large, intrusive noise in the qubit. Typically, the tunnel resistance is of the order of 100 kxcexa9.
Alternative embodiments of the invention can place the electrodes symmetrically or asymmetrically over the junction. Asymmetric placement further allows for the readout of a dipole magnetic field inside the junction, with the Hall electrodes being predominantly sensitive to one dipole component.
The four-terminal readout process does not introduce a strong coupling to the environment and is compatible with the qubit schematics. Additionally, fabrication techniques permit formation of the readout system as part of an integrated structure that can be scaled to include a large number of qubits.